Thiago Silva – who will be suspended for the semi-final in Belo Horizonte – bundled in the opener just seven minutes in, and Luiz hammered in a stunning free-kick to make it 2-0 in the second half.
Colombia pulled back a penalty through James Rodriguez with 12 minutes left to set up a nerve-wracking finale for the host nation but they held on.
The nation now awaits news on the fitness of striker Neymar, who was stretchered off and taken to hospital after being on the receiving end of a knee in the back.
Former Chelsea defender Luiz said: "I want to congratulate both teams for this great game - Colombia made a great World Cup and fought until the end. Our team played beautiful football that everyone likes, with a lot of intensity, seeking the goal every moment.
"It will be another great game against Germany, a world derby. I hope that we can be at our best level as they have a great team.
"They always play the same way with a lot of consistency. It will be another beautiful game."
Skipper Thiago blamed himself for the yellow card which means he will sit out the Germany clash.
"The card makes me miss the (next) game, but Dante and Henrique are fully capable of playing well and replace me. It was silly as I was returning to defend, the goalie threw the ball in my front and I didn't have any way to leave. I don't even know if the (referee's) interpretation was correct."
Chelsea midfielder Oscar added: "We played well - we deserved the 1-0 lead in the first half, or even more. We started well in the second half, wasted some chances, scored for 2-0 and then due to a mistake gave away a penalty.
"We knew how to control and win the game, our passing was much better today and we created many chances, our whole team played well and when everyone plays well, it's much easier. Our team is very good and we will do everything to win this World Cup."